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Anita wants to prove a diagonal of a rhombus PQRS bisects its vertex angles. She uses triangles PQR and PSR with PQ = QR = RS = SP and PR common.
Which rule proves the two triangles congruent so the diagonal bisects the angles?

Class 9SSS and RHS CongruenceGeometry — Triangles
  • ASSS
  • BRHS
  • CAAA
  • DSSA

Step-by-Step Solution

In a rhombus all sides are equal, so PQ = PS, QR = SR, and PR = PR (common). SSS proves triangle PQR ≅ triangle PSR; by CPCT the diagonal PR bisects angles P and R.
Answer: A) SSS

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